Financial Seismic Risk Assessment of Reinforced Concrete Bridge Piers using a Distribution-Free Approach

R.P. Dhakal, J.B. Mander and K. Solberg

Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand

Presented at New Zealand Society for Earthquake Engineering Annual Conference (NZSEE06), New Zealand, 2006.

Expected annual loss (EAL), which can be expressed in dollars, is an effective way of communicating the seismic vulnerability of constructed facilities to owners and decision makers. A concise method for computing Expected annual loss (EAL) without the inherent bias of requiring a specific analytical probability distribution is presented. The relationships between intensity measures and engineering demand parameters resulting from an Incremental Dynamic Analysis are sorted into fractal intervals by way of spectral reordering and modified to incorporate additional sources of uncertainty and randomness. Damage measures are defined to determine thresholds for damage states. Damage is quantified by loss ratios defined as repair cost divided by replacement cost. The results are numerically integrated to give Expected annual loss (EAL). An example illustrating the method is performed, comparing the seismic vulnerability of two highway bridge piers; one pier traditionally designed for ductility, and the other designed for damage avoidance. The damage avoidance pier has a clear advantage over the conventional pier, with an Expected annual loss (EAL) some 85% less than its ductile counterpart. This is shown to be primarily due to its inherent damage-free behaviour for almost all ground motions, except for very rare events that could potentially lead to toppling.

To perform the Incremental Dynamic Analysis (IDA), a non-linear structural model was developed. A pier most likely to be critical to the structure was idealized as a SDOF system; i.e. a lumped mass centreline column with rotational springs at its base. The hysteretic properties of the springs were calibrated based on experimental testing. The ductile pier was modelled using a Takeda hysteretic loop and strength degradation after ductility of 8. Using the multi-spring principles of modelling, as given in the original DRAIN-2DX software for this class of precast concrete structure (Prakash et al. 1992), the DAD pier was modelled using two springs; one spring representing the bi-linear elastic behaviour inherent in post-tensioned rocking systems and a second elasto-plastic spring representing energy dissipation.

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